On smooth surfaces in P4 containing a plane curve
Abstract
Description
We consider smooth surfaces $S \subset \Pq$ containing a plane curve $P$ and prove some general result concerning the linear system $|H-P|$. We then look at regular surfaces lying on hypersurfaces of degree $s$ having a plane of multiplicity $(s-2)$. This implies that $S$ contains a plane curve. We prove that the degree of such surfaces is bounded and for $s=4$ we compute an actual bound.
10 pages. The content has been replaced since there was an error in the proof of the main theorem
10 pages. The content has been replaced since there was an error in the proof of the main theorem